xvi, 230 p. : 25 cm

Includes bibliographical references (p. [216]-220) and indexes

Measure Theory -- [sigma]-algebras and their generators -- Dynkin systems -- Contents, premeasures, measures -- Lebesgue premeasure -- Extension of a premeasure to a measure -- Lebesgue-Borel measure and measures on the number line -- Measurable mappings and image measures -- Mapping properties of the Lebesgue-Borel measure -- Integration Theory -- Measurable numerical functions -- Elementary functions and their integral -- The integral of non-negative measurable functions -- Integrability -- Almost everywhere prevailing properties -- The spaces L[superscript p]([mu]) -- Convergence theorems -- Applications of the convergence theorems -- Measures with densities: the Radon-Nikodym theorem -- Signed measures -- Integration with respect to an image measure -- Stochastic convergence -- Equi-integrability -- Product Measures -- Products of [sigma]-algebras and measures -- Product measures and Fubini's theorem -- Convolution of finite Borel measures -- Measures on Topological Spaces -- Borel sets, Borel and Radon measures -- Radon measures on Polish spaces -- Properties of locally compact spaces -- Construction of Radon measures on locally compact spaces -- Riesz representation theorem -- Convergence of Radon measures -- Vague compactness and metrizability questions

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